anonymous
  • anonymous
Rationalize the denominator square root of 20/x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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agreene
  • agreene
are you asking \(\large\sqrt{\frac{20}{x}}\)
anonymous
  • anonymous
yes
anonymous
  • anonymous
i have the answer, i just don't know how to get it

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agreene
  • agreene
Well, I was going to say I dont know what exactly they're wanting, because it doesnt really make sense...
agreene
  • agreene
\[2\sqrt{5}\sqrt{x^{-1}}\] is how I would answer, but its not "Rationalizing the denominator"
anonymous
  • anonymous
\[\frac{ 2\sqrt{5x} }{ x }\] is the answer
anonymous
  • anonymous
i just don't get why x is in the numerator
agreene
  • agreene
I got there like this: \[\sqrt{\frac{20}{x}} = \sqrt{20}\sqrt{-1} = 2\sqrt{5} \sqrt{x^{-1}}\]
agreene
  • agreene
Well, I suppose it's true if x is always positive... but it's technically wrong.
anonymous
  • anonymous
thank you for your help!
agreene
  • agreene
\[\sqrt{\frac{20}{x}}=\frac{\sqrt{20}}{\sqrt{x}} = \frac{2\sqrt{5}}{\sqrt{x}}\]
anonymous
  • anonymous
YESSS that has to be right.
agreene
  • agreene
that x with the 5 is to keep it from being 0/0
agreene
  • agreene
but technically, they arent the same.
anonymous
  • anonymous
so does the x have to be written?
agreene
  • agreene
I mean, if you're instructor requires it... lol
anonymous
  • anonymous
If x is not a perfect square the denominator will be irrational, so multiplying and dividing by a factor of square root of x will rationalize the denominator
anonymous
  • anonymous
Feels rather unnecessary though
triciaal
  • triciaal
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triciaal
  • triciaal
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triciaal
  • triciaal
when you rationalize the denominator you are getting rid of the radical in the denominator. you multiply by a factor of one (expressed as fraction with radical) look again at the drawing then simplify

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